Prove Existence of Borel Measure with Compact Set as Support in R

[StatusX]

Let m be a measure on the space X. I'm told that if m(X)=1, K is a compact subset of X with m(K)=1, and K has the property that any proper compact subsets of K have measure strictly less than 1, then K is called the support of m. Then I'm asked to show that every compact subset of R is the support of some Borel measure.

Does this mean that given a compact set K in R, there exists a Borel measure m with m(R)=m(K)<infinity and m(L)<m(K) for any proper compact subset L of K? If so, I'm having a hard time understanding what such a measure would look like, or how I would prove one exists. Can anyone help me here?

 

[StatusX]

Never mind, I got it (it involved a dense countable subset of K).